BRIEF PAPER Accurate Permittivity Estimation Method for 3-Dimensional Dielectric Object with FDTD-Based Waveform Correction

Transcription

1 IEICE TRANS. ELECTRON., VOL.E97 C, NO.2 FEBRUARY BRIEF PAPER Accurae Permiiviy Esimaion Mehod for 3-Dimensional Dielecric Objec wih FDTD-Based Waveform Correcion Ryunosuke SOUMA, Shouhei KIDERA a, and Tesuo KIRIMOTO, Members SUMMARY Ulra-wideband pulse radar exhibis high range resoluion, and excellen capabiliy in peneraing dielecric media. Wih ha, i has grea poenial as an innovaive non-desrucive inspecion echnique for objecs such as human body or concree walls. For suiabiliy in such applicaions, we have already proposed an accurae permiiviy esimaion mehod for a 2-dimensional dielecric objec of arbirarily shape and clear boundary. In his mehod, he propagaion pah esimaion inside he dielecric objec is calculaed, based on he geomerical opics GO approximaion, where he dielecric boundary poins and is normal vecors are direcly reproduced by he range poin migraion RPM mehod. In addiion, o compensae for he esimaion error incurred using he GO approximaion, a waveform compensaion scheme employing he finie-difference ime domain FDTD mehod was incorporaed, where an iniial guess of he relaive permiiviy and dielecric boundary are employed for daa regeneraion. This sudy inroduces he 3-dimensional exension of he above permiiviy esimaion mehod, aimed a pracical uses, where only he ransmissive daa are effecively exraced, based on quaniaive crieria ha considers he spaial relaionship beween anenna locaions and he dielecric objec posiion. Resuls from a numerical simulaion verify ha our proposed mehod accomplishes accurae permiiviy esimaions even for 3-dimensional dielecric medium of wavelengh size. key words: UWB pulse radar, permiiviy esimaion, non-desrucive esing, non-invasive inspecion, 3-D image reconsrucion, range poins migraion RPM mehod 1. Inroducion There are various demands for an innovaive hreedimensional 3-D imaging echnique for objecs embedded in dielecric media, aimed a highly reliable and noninvasive human body screening for medical purposes or he prevenion monioring of arificial srucures o reduce a damage from naural caasrophes. As one of he mos promising echniques ha could saisfy hose demands, elecro-magneic sensor sysems using UWB Ulra Wideband signals come highly recommended, because i has sufficien range resoluion and he desired dielecric peneraing capabiliy. To dae, various kinds of inernal imaging approaches for dielecric objecs have been esablished. These are mainly classified ino wo schemes. One is he posiioning or shape reconsrucion scheme for objecs buried in dielecric media using refocusing echniques such as space-ime Manuscrip received July 25, Manuscrip revised Ocober 23, The auhor is wih Kyosan Elecric Manufacuring Co., Ld., Yokohama-shi, Japan. The auhors are wih he Graduae School of Informaics and Engineering, The Universiy of Elecro-Communicaions, Chofushi, Japan. a kidera@ee.uec.ac.jp DOI: /ransele.E97.C.123 beamforming [1] or ime-reversal focusing [2], aimed a he deecion of umors or unexploded buried landmines. However, hese echniques are no necessarily suiable in idenifying 3-D objecs wih clear boundaries, because hese only provide a number of 2-dimensional 2-D grayscale images, and require appropriae pos-processing o reconsruc he accurae high-resoluion 3-D image. The oher scheme is mainly based on inverse scaering analysis using he domain inegral equaions [3]. Alhough his scheme direcly reconsrucs he spaial disribuion of he dielecric consan even in inhomogeneous media, is accuracy or spaial resoluion srongly depends on he assumed pixel size direcly relaed o he number of opimizaion variables. Also, o avoid sluggish convergence in muli-dimensional opimizaions. here is a severe consrain on space discreizaion size. In conras, he mehod in [4], aimed a hrough-hewall applicaions, requires relaively smaller compuaional resources compared wih mehods described in [3] hrough use of he geomerical opics GO approximaion. However, implemenaion of he mehod assumes he srucures of he dielecric media are known and simple, such as recangles. As an effecive soluion for he above issue, we have already developed an innovaive mehod, which simulaneously accomplishes accurae inernal 2-D imaging and permiiviy esimaion [5]. This mehod employs he original RPM mehod [6] o correcly produce he dielecric boundary posiions and heir normal vecors. The acual ime delay in propagaing hrough he dielecric medium can hen be accuraely esimaed from he recorded ransmissive daa. In paricular, locaion and shape of an inernal objec are direcly reconsruced by combining he exiing inernal imaging mehod [8], which requires a correc dielecric consan for a surrounding dielecric objec o accomplish highly accurae inernal arge reconsrucion. This sudy exends he exising permiiviy esimaion mehod [5] o he 3-D problem wih an appropriae observaion model. In his model, he ransmissive and direc signals should be correcly discriminaed wihou using aprioriinformaion of he dielecric objec, while he effec of direc wave is negligible in he former 2-D model described in [5]. For his purpose, his mehod inroduces quaniaive crieria, which are calculaed from he spaial relaionship beween an esimaed dielecric shape by RPM and he ransmiing and receiving anenna locaions. Moreover, for dielecric medium of wavelengh scale, he ransmissive waveform differs from he ransmied waveform, and i reduces Copyrigh c 2014 The Insiue of Elecronics, Informaion and Communicaion Engineers

2 124 IEICE TRANS. ELECTRON., VOL.E97 C, NO.2 FEBRUARY 2014 Fig. 1 Sysem model in 3-D problem. Fig. 2 Discriminaion of direc and ransmissive signal by he spaial relaionship of he firs Fresnel zone and he dielecric objec posiion. he accuracy of he ime-delay measuremen. Then, his exension also includes he waveform compensaion process by regeneraing he observaion daa using a finie-difference ime domain FDTD mehod, similar o ha given in [5]. The numerical-simulaion-based validaions show ha our mehod provides accurae permiiviy esimaions, by aking a compleely non-parameric approach even for 3-D arges of wavelengh scale. 2. Sysem Model Figure 1 shows he sysem model. I assumes ha arge and dielecric medium have an arbirary 3-D shape wih clear boundaries. The dielecric objec is a homogeneous, nondispersive, and lossy medium. One omni-direcional ransmiing and receiving anenna is locaed a r TR = X, Y, Z, he oher anenna funcioning only as a receiver is locaed a r R = X, Y, Z. The pair of wo anennae are scanned along a circle on he z = Z plane, cenered on he z axis wih radius is R c = X 2 + Y 2. A number of circular scannings on differen z planes is performed, namely, hose over he cylindrical surface wih he z axis cenering as shown in Fig. 1. A mono-cycle pulse is used as he ransmiing signal, he cener wavelengh of which is defines as λ. S TR r TR, R and S R r R, R are defined as he oupu of he Wiener filer a anenna posiion r TR and r R, respecively where R = c/2 is expressed by ime and he propagaion speed of he radio wave c. 3. Proposed Permiiviy Esimaion Mehod In [5], we have already discussed and verified ha mehod [5] holds some advanages over exising approaches given in [3] or [4]. To avoid repeiion, his leer forhwih inroduces he 3-D exension of our previous mehod [5]. 3.1 Dielecric Boundary Exracion by RPM Similar o he 2-D approach, his mehod firs em- ploys he dielecric boundary poins exraced by he RPM mehod [6], which achieves accurae imaging employing he observed range poins defined as q DR,i = XDR,i, Y DR,i, Z DR,i, R DR,i, i = 1,..., NDR DR denoes dielecric reflecion. These poins are exraced from he maxima of S R r DR, R. Nex, he RPM mehod direcly convers hese range poins o he dielecric boundary poins as r i = x i,y i, z i, i = 1,...,N DR, wih he conversion being one-o-one. The normal vecors for all boundary poins are direcly calculaed wihou he derivaive operaion as e n,i = X DR,i x i, Y DR,i y i, Z DR,i z i /R DR,i. In addiion, o obain arge poins and normal vecors on he dielecric boundary wih a sufficienly small inerval, he Envelope inerpolaion described in [7] and [8] is also inroduced. Boh boundary poins and normal vecors are necessary for he proposed permiiviy esimaion scheme, paricular in esimaing he propagaion pah inside he dielecric medium. 3.2 Discriminaion of Direc and Transmissive Signals Here, i should be noed ha he received signal S R r R, R includes boh componens of he direc and ransmissive signals. The direc signal comprises a received componen ha propagaes along a dielecric surface, called he creeping wave which does no penerae he dielecric medium. The ransmissive signal is regarded as a received componen ha peneraes he dielecric medium ha should be aken ino accoun in he permiiviy esimaion. Depending on he paricular spaial relaionship among he ransmiing, receiving anennas, and dielecric objec posiion, S R r R, R migh be dominaed by he direcly propagaed componen, and his signal should no be considered in he permiiviy esimaion processing. To address he above issue, his sudy inroduces he discriminaion scheme beween he direc and ransmissive signals, based on he quaniaive crieria deermined by he spaial relaionship beween he firs Fresnel zone and he esimaed dielecric boundary poins, obained by he RPM as previously described. This crieria qualiaively indicaes ha if he firs Fresnel zone deermined by he ransmiing and receiving anenna locaions is largely

3 BRIEF PAPER 125 occupied by he dielecric medium, he dominan componen of he received signal in such an observaion geomery should be classified as a ransmissive signal. In his case, o esablish quaniaive crieria, he following index is inroduced, ζ Fres q R = A Oq R, T rpm, 1 A T q R where q R = X R, Y R, Z R, R R denoes he range poin, which is exraced from he maxima of S R r R, R anda T q R denoes he oal surface of he circle on he biseced plane called he biseced circle by he line beween he ransmiing anenna and he receiving anenna, he region of which is deermined by he firs Fresnel zone. A O q R, T rpm denoes he projeced region on he biseced circle, which is deermined by he line of sigh from each anenna locaion X TR, Y TR, Z TR orx R, Y R, Z R o he esimaed dielecric boundary poins denoed as T rpm. If ζ Fres q R >ζ h holds, he q R is classified ino he ransmissive range poin and is used in he permiiviy esimaion, which follows. 3.3 Permiiviy Esimaion wih Transmissive Signal To esimae he dielecric consan for an objec, his mehod minimizes he difference beweenan observedand esimaed propagaion ransmissive delay. Here, he relaive permiiviy is deermined by ɛ ini = arg min ɛ R ɛ : X DT,i, Y DT,i, Z DT,i RDT,i, 2 where q DT,i = X DT,i, Y DT,i, Z DT,i, R DT,i, i = 1,..., NDT denoing he ransmissive range poins DT denoes dielecric ransmission, which saisfy he crieria menioned in Sec. 3.2 on he se of q R. R ɛ : X DT,i, Y DT,i, Z DT,i is he esimaed propagaion delay using he RPM boundary poins and normal vecors deermined by he GO approximaion. The procedure for he propagaion pah esimaion is deailed in [5] for he 2-D model, bu can be naurally exended o he 3-D model by an appropriae variable exension. Using all he ransmissive range poins, he iniial relaive permiiviy ˆɛ ini ˆɛ ini = { where Q = is esimaed nex from Q S R ɛ ini q DT,i ɛ ini Q S R, 3 ɛ ini } < Δɛ ini,and ɛ ini is he, mode value calculaed from he disribuion of ɛ ini is he hreshold o eliminae ouliers. Δɛ ini Noe ha he above procedure is basically derived from he GO approximaion, where he frequency characerisic in ransmissive phenomena is no aken ino consideraion. However, for a dielecric medium of wavelengh scale, his frequency characerisic is no negligible and causes waveform deformaion of he ransmissive daa, reducing he accuracy of he relaive permiiviy esimaion, hrough inaccuracy in he range poins. Fig. 3 Flowchar of he proposed mehod. are employed for FDTD daa generaion. Nex, he range correcion ΔR q DT,i a each range poin q DT,i is deermined from he peak shif of he correlaion funcion beween he measured S DT r DT, R and he regeneraed ransmissive daa S DT r DT, R. The compensaed relaive permiiviy ɛ for each range poin is calculaed as To compensae for he range errors caused by he waveform discrepancy beween he ransmied and ransmissive waveform, he FDTD daa regeneraion is applied using he iniial guess of he permiiviy and dielecric objec. The deail of he approach are also he same in he 2-D model referred o in [5]. Specifically, we regenerae he ransmissive daa as S R r DT, R using he FDTD, where he dielecric boundary poins as T rpm and he esimaed relaive permiiviy as ˆɛ ini ɛ = ˆɛ ini + ΔR 2 L ɛ, 4 where L ɛ is he esimaed propagaion disance in he dielecric medium for q DT,i and ˆɛ ini is he iniial relaive permiiviy esimaed by he weighed average of ɛ ini. Finally, he relaive permiiviy ˆɛ is deermined hrough a weighed average similar o ha given in Eq. 3. Noe ha, he esimaion error for he permiiviy esimaion is mosly compensaed for in he FDTD daa regeneraion only once, because he range errors are mainly caused by he frequency characerisic depending on he dielecric shape; he small error in he permiiviy is negligible in regard o error compensaion for each range poin. Figure 3 shows a flowchar of he acual procedure for our proposed mehod. 4. Performance Evaluaion of Numerical Simulaion This secion presens performance validaion of he proposed mehod, where he observaion daa are creaed by employing he FDTD mehod. Here, he dielecric objec and he inernal arge shape are used as shown in Fig. 1. The boundary of he dielecric objec is expressed as he ellipsoid x/1.5λ 2 + y/1.0λ 2 + z/2.5λ 2 = 1 holds, and ha of he inernal objec is expressed as x/0.5λ 2 + y/0.5λ 2 +

4 126 IEICE TRANS. ELECTRON., VOL.E97 C, NO.2 FEBRUARY 2014 Fig. 4 Hisograms of esimaed relaive permiiviy before lef and afer righ WC a S/N = 30 db. shape of he dielecric objec, which is ellipse a he cross secion on he x y plane. Noe also ha here is an invisible area in he arge boundary because he range poins from his shadow area are no rerieved, owing o a disored propagaion pah depending on dielecric boundary shape. However, his resul shows ha our proposed permiiviy esimaion is promising for accurae inernal 3-D imaging wihou using he aprioridielecric consan or shape informaion. Finally, i should be noed ha, in he ypical nondesrucive model, a shape of dielecric objec and buried objec would be cylindrical one, which is differen from he model assumed in his leer. Since he cylindrical arge model is almos equivalen o he 2-dimensional problem, is effeciveness can be analogized from he resuls obained in he previous work [5]. Then, his leer assumes he ellipsoidal dielecric and buried objecs o assess he proposed mehod in he fully 3-dimensional model, where he propagaion pah based on GO approximaion should be curved along z axis. 5. Conclusion Fig. 5 Esimaed inernal image a S/N = 30 db. z/0.75λ 2 = 1 holds. The conduciviy of he inernal arge is se o S/m, and he conduciviy and relaive permiiviy of he dielecric medium are se o 0.01 S/m and ɛ = 5.0, hose values of which are ypical for he case ha a meallic pipe is buried in a concree body. Whie Gaussian noise is added o S TR X, Y, Z, R ands R X, Y, Z, R, where he signal-o-noise raio S/N is defined as he raio of he peak insananeous signal power o he average noise power afer applying he mached filer. r c = 0, 0 and R c = 2.5λ are se, and he sample scanning for he anenna involves 51 in he x y plane and 40 along z-axis uniformly spaced poins. Δɛ ini = 0.5andζ h = 0.95 are se in his case. Figure 4 presens hisograms of he esimaed relaive permiiviy a S/N=30 db, obained a each range poin before and afer waveform compensaion abbreviaed as WC. As shown in his figure, he mean and sandard deviaions of he esimaed relaive permiiviy are considerably improved by he waveform correcion of Eq. 4. The esimaed relaive permiiviies before and afer WC are ˆɛ ini = 4.74 relaive error: 5.2 % and ˆɛ = 4.98 relaive error: 0.4 %. These resuls demonsrae ha he waveform correcion approach is considerably effecive. Figure 5 shows he inernal arge boundary poins esimaed using he mehod described in [8] and using he esimaed permiiviy wih he proposed mehod. This figure visually verifies ha he par of he inernal esimaion image is correcly reconsruced by using he accuraely esimaed dielecric consan. The asymmeric view of he obained inernal image is due o he Our sudy exended he former permiiviy esimaion mehod o a 3-D observaion model, where suiable modificaions were inroduced, paricularly in discriminaing he ransmissive and direc signals by esablishing quaniaive crieria. This mehod has a significan advanage over convenional echniques, and i is applicable o arbirary unknown dielecric boundary shapes, and hus does no require any prior informaion such as dielecric consan or shape. In numerical simulaions based on he FDTD mehod, our mehod reduced he relaive errors in he relaive permiiviy esimaion o less han 1%, even for he S/N = 30 db daa from an ellipsoidal dielecric medium. As a resul, he inernal image obained employing he exising echnique described in [8] provides a correc arge shape even from noisy daa. References [1] X. Li, E.J. Bond, B.D. Van Veen, and S.C. Hagness, An overview of ulra-wideband microwave imaging via space-ime beamforming for early-sage breas-cancer deecion, IEEE Anennas Propag. Mag., vol.47, no.2, pp.19 34, Feb [2] P. Kosmas and C.M. Rappapor, A mached-filer FDTD-based ime reversal approach for microwave breas cancer deecion, IEEE Trans. Anennas Propag., vol.54, no.4, pp , April [3] A. Franchois and C. Picho, Microwave imaging-complex permiiviy reconsrucion wih a Levenberg-Marquard mehod, IEEE Trans. Anennas Propag., vol.45, no.2, pp , Feb [4] J. Ren, Y. Zhang, T. Jiang, and W. Chen, Esimaion of wall parameers from ime-delay-only hrough-wall radar measuremens, IEEE Trans. Anennas Propag., vol.59, no.11, pp , Nov [5] R. Souma, S. Kidera, and T. Kirimoo, Accurae permiiviy esimaion mehod wih ieraive waveform correcion for UWB inernal imaging radar, IEICE Trans. Elecron., vol.e96-c, no.5, pp , May [6] S. Kidera, T. Sakamoo, and T. Sao, Accurae UWB radar hreedimensional imaging algorihm for a complex boundary wihou range poin connecions, IEEE Trans. Geosci Remoe Sens., vol.48, no.7,

5 BRIEF PAPER 127 pp , April [7] S. Kidera, T. Sakamoo, and T. Sao, High-resoluion and real-ime UWB radar imaging algorihm wih direc waveform compensaions, IEEE Trans. Geosci. Remoe Sens., vol.46, no.11, pp , Nov [8] K. Akune, S. Kidera, and T. Kirimoo, Accurae and nonparameric imaging algorihm for arges buried in dielecric medium for UWB radars, IEICE Trans. Elecron., vol.e95-c, no.8, pp , Aug